确定逻辑约束问题的一种通用方法

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摘要翻译：
给出了一种修正信度并对逻辑约束问题系统作出一致决策的一般方法。与其他关于信念修正的工作不同，这里的约束假设是固定的。该方法有两个变体，相互对偶，修正后的信度分别高于和低于原信度。上[下]修正信度被唯一地表征为由逻辑约束确定的某个max-min[下-min-max]操作不变的最低[下]修正信度。在这两种变体中，在一个命题的修正的信念程度和它的否定的信念程度之间取得平衡会导致确保与逻辑约束相一致的决定。只要给出一致的结果，这些决定就会与适用于原始信念程度的多数准则相一致。它们还被确保满足对任何特定问题的一致尊重的性质，以及对原始信仰程度的单调性的性质。该方法在某些特殊领域的应用可以归结为一些成熟的或日益被接受的方法，如聚类分析中的单链路方法和优先投票中的路径方法。
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英文标题：
《A general method for deciding about logically constrained issues》
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作者：
Rosa Camps, Xavier Mora, Laia Saumell
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最新提交年份：
2012
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
  A general method is given for revising degrees of belief and arriving at consistent decisions about a system of logically constrained issues. In contrast to other works about belief revision, here the constraints are assumed to be fixed. The method has two variants, dual of each other, whose revised degrees of belief are respectively above and below the original ones. The upper [resp. lower] revised degrees of belief are uniquely characterized as the lowest [resp. highest] ones that are invariant by a certain max-min [resp. min-max] operation determined by the logical constraints. In both variants, making balance between the revised degree of belief of a proposition and that of its negation leads to decisions that are ensured to be consistent with the logical constraints. These decisions are ensured to agree with the majority criterion as applied to the original degrees of belief whenever this gives a consistent result. They are also also ensured to satisfy a property of respect for unanimity about any particular issue, as well as a property of monotonicity with respect to the original degrees of belief. The application of the method to certain special domains comes down to well established or increasingly accepted methods, such as the single-link method of cluster analysis and the method of paths in preferential voting.
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PDF链接：
https://arxiv.org/pdf/1007.2534

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